Nanoparticles coated with DNA molecules can be programmed to self-assemble into three-dimensional superlattices. Such superlattices can be made from nanoparticles with different functionalities and could potentially exploit the synergetic properties of the nanoscale components. However, the approach has so far been used primarily with single-component systems. Here, we report a general strategy for the creation of heterogeneous nanoparticle superlattices using DNA and carboxylic-based conjugation. We show that nanoparticles with all major types of functionality--plasmonic (gold), magnetic (Fe2O3), catalytic (palladium) and luminescent (CdSe/Te@ZnS and CdSe@ZnS)--can be incorporated into binary systems in a rational manner. We also examine the effect of nanoparticle characteristics (including size, shape, number of DNA per particle and DNA flexibility) on the phase behaviour of the heterosystems, and demonstrate that the assembled materials can have novel optical and field-responsive properties.